Solve for $x$ and $y$ using elimination. ${6x+4y = 66}$ ${-5x+5y = -5}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $6$ ${30x+20y = 330}$ $-30x+30y = -30$ Add the top and bottom equations together. $50y = 300$ $\dfrac{50y}{{50}} = \dfrac{300}{{50}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {6x+4y = 66}\thinspace$ to find $x$ ${6x + 4}{(6)}{= 66}$ $6x+24 = 66$ $6x+24{-24} = 66{-24}$ $6x = 42$ $\dfrac{6x}{{6}} = \dfrac{42}{{6}}$ ${x = 7}$ You can also plug ${y = 6}$ into $\thinspace {-5x+5y = -5}\thinspace$ and get the same answer for $x$ : ${-5x + 5}{(6)}{= -5}$ ${x = 7}$